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Existence and nonexistence of solutions for an approximation of the Paneitz problem on spheres.
- Source :
- Boundary Value Problems; 10/23/2023, Vol. 2023 Issue 1, p1-14, 14p
- Publication Year :
- 2023
-
Abstract
- This paper is devoted to studying the nonlinear problem with slightly subcritical and supercritical exponents (S ± ε) : Δ 2 u − c n Δ u + d n u = K u n + 4 n − 4 ± ε , u > 0 on S n , where n ≥ 5 , ε is a small positive parameter and K is a smooth positive function on S n . We construct some solutions of (S − ε) that blow up at one critical point of K. However, we prove also a nonexistence result of single-peaked solutions for the supercritical equation (S + ε) . [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 16872762
- Volume :
- 2023
- Issue :
- 1
- Database :
- Complementary Index
- Journal :
- Boundary Value Problems
- Publication Type :
- Academic Journal
- Accession number :
- 173147961
- Full Text :
- https://doi.org/10.1186/s13661-023-01789-0